S15NMR

Pulsed Nuclear Magnetic Resonance!

Abstract

The purpose of our experiment was to explore the technique and application of pulsed nuclear magnetic resonance. To do so we introduced a pulsed radio frequency to target the hydrogen nuclei of a sample in a magnetic field to create excitation of the nuclear spin magnetization. The decay of this excitation toward an equilibrium state is described by two parameters known as the relaxation time constants T1 and T2, also known as the spin-lattice and spin-spin relaxation time. It is these times that are measured and analyzed for various concentrations of distilled water and glycerol. We found that these relaxation times range from T1, T2 values of 2:405 . 0:005 s, 1:361 . 0:012 s for 100% distilled water to 0:032 . 0:001 s, 0:017 . 0:001 s for 100% glycerol.

Theory

A sample is exposed to a magnetic field once its placed within the sample coil. Due to the Zeeman effect, the sample undergoes an energy state split that is equivalent

where is the Larmor Frequency. By definition of the experiment, the magnetic field is always in the while measurements only happen in the xy-plane.

Initially, the system is in equilibrium. Here the net magnetization points in the same direction as the magnetic field. And then, an RF signal (at the Larmor frequency) is sent to the sample through the sample coil. The magnetization vector is knocked off equilibrium.

Sending in a pulsed signal allows a specific rotation of the magnetization vector.

The length of the pulse determines the amount of rotation. After the pulse is over, the system returns toward thermal equilibrium and emits a free induction decay signal (FID). The FID is used to determine the relaxation time constants.

A 180 degree pulse is defined as the pulse length required such that the FID reaches its first minimum - the magnetization vector is now in the -

and measurements cannot be read by the sample coil. The 90 degree pulse is defined to be half the 180 degree pulse, or when the FID reaches its first maximum due to the components of magnetization vector being fully in the xy-plane where the sample coil can pick up all the data.

T1: Spin-lattice (longitudinal) Relaxation

T1 is the rate at which the disturbed magnetization returns to thermal equilibrium by transferring energy from the spin system to its surroundings (known as the lattice) [1].

T1 is measured by a two-pulse sequence called the inversion recovery method, and is done using 180 pulse followed by a 90 after some time %$ \tau $%. The plot of the FID amplitude vs.

is acquired and then analyzed to fit , which was derived from the Bloch equation. Here M(t) is the amplitude at time t, and

is the initial amplitude at thermal equilibrium.

The process can be seen below:

T2: Spin-spin (transverse) Relaxation

T2 is the exponential loss of transverse magnetization, or the time it takes the neighboring spins to lose coherence in their interactions with each other [1].

T2 is measured using two-pulse sequence to create a spin-echo, and is done using 90 pulse followed by a 180 after some time

. The plot of the FID amplitude vs.

is acquired and then analyzed to fit, which was also derived from the Bloch equation. Here M(t) is the amplitude at time t, and

is the initial amplitude at thermal equilibrium, and D is set to be a constant that is made up of the material's diffusion coefficient, the gyromagnetic ratio, and the spatial magnetic field gradient.

The process can be seen below:

(Image courtesy of Gavin W Morley, BA, MA (Oxon), MRes, DPhil, MInstP)

Equipment: TeachSpin PS2-B Spectrometer

Results

References

[1] Farrar, Thomas C. & Becker, Edwin D. (1971) Pulsed Fourier Transform NMR. New York, New York: Academic Press, Inc.

Additional References

    • TeachSpin PS2 Pulsed/CW NMR Manual.

    • Gri ths, D. J. (1995) Introduction to Quantum Mechanics (2nd Edition). Upper Saddle River, NJ: Prentice Hall, Inc.

    • H. Y. Carr & E.M. Purcell (1954). E.ects of Di.usion on Free Precession in Nuclear Magnetic Resonance Experiments. Physics Review, 94(3), pp. 630{638.

    • F. Bloch (1946). Nuclear Induction. Physics Review, 70(7), pp. 460-474.

    • L. Bianchini & L. Co.ey (2010). NMR Techniques Applied to Mineral Oil, Water, and Ethanol. Brandeis University, MA, 02453.

    • N. Bloembergen, E. M. Purcell, and R. V. Pound (1948) Relaxation E.ects in Nuclear

    • Magnetic Resonance Absorption. Physical Review 73, 679. "The Nobel Prize in Physics 1952". Nobelprize.org. Nobel Media AB 2014. Web. 9 May 2015. <http://www.nobelprize.org/nobel_prizes/physics/laureates/1952/>

    • Steinberg, E., & Cohen, A. (1984). Nuclear magnetic resonance imaging technology: A clinical, industrial, and policy analysis. Washington, D.C.: Congress of the U.S., Office of Technology Assessment. p. 15.

    • Levitt, M. (2008). 11.9 Free Evolution with Relaxation. In Spin dynamics: Basics of nuclear magnetic resonance (Second ed.). The University of Southampton: Wiley.

    • Hahn EL (1950) Spin echoes. Phys Rev;80:580-594.

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